Mohamed Salah scored a stoppage-time penalty against Burnley on Sunday as Liverpool maintained their perfect record to return to the top of the Premier League.
Erling Haaland struck twice as Manchester City inflicted another damaging defeat on Manchester United boss Ruben Amorim with a comprehensive 3-0 win.
Scott Parker's men had doggedly kept the champions at bay but a Hannibal Mejbri handball in the dying seconds gave Salah a chance to win the match and he made no mistake.
Liverpool are the first side in Premier League history to win four consecutive games with winning goals scored in the final 10 minutes or later -- with Sunday's coming in the 95th minute.
They are three points clear of Arsenal, who went top of the table on Saturday with a 3-0 win against Nottingham Forest.
Arne Slot's Liverpool, chasing a record 21st English league title, have not been at their best this season but have found a way to win all four of their matches.
The Dutchman said his team had struggled to create clear-cut chances against a side who defended deep.
They had 27 shots at Turf Moor but just four of those were on target.
"We kept playing, we kept moving the ball around," Slot told Sky Sports. "They got more and more tired which is normal when you have to defend for 80 percent of time and then we got as many attackers on as possible.
"Difficult game but all of them are in the Premier League. A clean sheet and from open play we hardly concede a chance. That's a good thing.
"It is normal and a lot of new players, we will get better and better but in the meantime we have 12 points."
Isak absent
Slot left new signing Alexander Isak out of his squad after warning he would ease the forward into action gradually.
But he could still field an impressive attacking line-up including Salah, Cody Gakpo, Florian Wirtz and Hugo Ekitike.
Liverpool dominated from the start while Burnley sought to break quickly on the rare occasions when they won possession.
Liverpool centre-back Ibrahima Konate headed over from close range and Ekitike flicked a shot wide of the far post from a narrow angle.
But their one shot on target in the first half came from Andy Robertson soon after he had replaced Milos Kerkez in the 38th minute.
The Hungary international had been booked for diving for a penalty, and Slot removed him from the fray after another foul to avoid a potential sending-off.
Ryan Gravenberch flashed a volley wide early in the second half and goalkeeper Martin Dubravka kept out a long-range effort from Dominik Szoboszlai.
Slot made his first attacking change in the 72nd minute, bringing on Federico Chiesa for Ekitike.
The move almost paid immediate dividends but the Italian international failed to direct his header from Robertson's cross on target.
Burnley were reduced to ten men as Lesley Ugochukwu was shown a second yellow card for bringing down Wirtz on the edge of the box in the 84th minute.
Slot threw on Jeremie Frimpong and Rio Ngumoha for Wirtz and Konate in a last-ditch bid for all three points.
Their relentless pressure finally paid off when Mejbri handled Frimpong's cross in the penalty area and referee Michael Oliver pointed to the spot.
Salah stepped up and blasted the ball into the net, ensuring a fourth win from four matches.
Burnley, promoted back to the Premier League in April, have one win and three defeats from their first four matches of the season.
Haaland keeps scoring
Phil Foden opened the scoring before Haaland took centre stage with a second-half double, either side of an incredible miss from the Norwegian, as City bounced back from two consecutive Premier League defeats.
United went into a derby ahead of City in the table for the first time in five years.
But that owed more to City's early season struggles than signs of progress for Amorim's men, who have taken just four points from their opening four games and been dumped out of the League Cup by fourth-tier Grimsby.
To cap a fine City display, goalkeeper Gianluigi Donnarumma marked his debut with a stunning save from Bryan Mbeumo to deny United a foothold in the game at 2-0.
City remain six points adrift of leaders Liverpool, but victory is a huge confidence boost for Pep Guardiola's side ahead of facing Serie A champions Napoli and Premier League title rivals Arsenal next week.
Before kick-off, both sets of fans put rivalry aside to pay tribute to boxing legend Ricky Hatton, who died on Sunday at the age of 46.
A massive City fan, Hatton's face was displayed on big screens during a minute's applause.
Foden, a fellow boyhood City supporter, said before kick-off the news gave the home side extra motivation to win in Hatton's honour.
And the England international was central to a much-needed victory after a difficult start to the campaign for Foden and City.
The 25-year-old was the Premier League player of the season in the 2023/24 campaign, but his form dipped drastically last season.
Fitness issues meant he had not started a game this season until Sunday, but took just 18 minutes to make his mark.
United's defence allowed Jeremy Doku to bundle his way to the by-line and the Belgian's cross picked out Foden, completely unmarked, to head in the opening goal.
Both goalkeepers were under the spotlight as Ruben Amorim kept faith with Altay Bayindir over new signing Senne Lammens.
Donnarumma decisive
Tijjani Reijnders fired straight at Bayindir when presented with the chance to quickly double City's advantage.
Doku was the creator once more when City did double their lead on 53 minutes.
Haaland showed his power, pace and incredible precision to dink the ball over the onrushing Bayindir.
City's number nine went from the sublime to the ridiculous moments later when he missed an open goal with the chance to double his tally.
United were architects of their own danger as Matthijs de Ligt's poor pass set up a City counter-attack.
Reijnders' dummy set Haaland clear on goal, but after rounding Bayindir, he could only hit the post on the stretch.
Moments later Donnarumma produced his moment of magic to prevent what could have been a turning point.
Mbeumo's sweetly-struck volley was arrowing into the bottom corner until the Italian reached out a giant right hand to turn it behind.
What could have been 2-1 was soon 3-0 thanks to another United gift.
Harry Maguire this time gave away possession to Bernardo Silva, who set Haaland racing away into the vacant United half and he kept his cool to score for the eighth time in nine appearances against United.
Reijnders should have rubbed further salt in the Red Devils' wounds when the Dutch international slotted wide with just Bayindir to beat.
But that did not stop the City fans goading Amorim with chants of "sacked in the morning".
The Portuguese is not in danger of an immediate dismissal, but his Premier League record now reads a dismal eight wins in 31 games.
